GP Rider Game Gear has a turbo button mapped to UP. You may remap this to a face button on a 3 button Genesis controller.

As in Super Hang-On, the game timer is bugged. What that means is whenever you finish a sector, the subseconds counter is not zeroed. Because of that, you'll need to subtract the fractions of seconds that show up after each checkpoint in Arcade Mode, to find your final time. So Africa, you just take the goal time and remove the five fractions that showed up, as these are double counted. Existing times have been edited to reflect that. I will always double check your final time but get into the habit of working that out yourself with a calc: the effect is that your 'lowest' finishing time may not actually be your lowest time, so scan over all your completed runs.

As for emulators, Fusion is banned. Please use Bizhawk or RetroArch.